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The time series of GNSS coordinates contain signals caused by the age-related movement of tectonic plates, the deformation of the Earth's surface, as well as errors at different time scales from sub-daily tidal deformation to the long-term deformation of the surface load. Depending on the nature of the signal, specific approaches are used for both the visual interpretation and pre-processing of time series and their statistical analysis. However, none of the present software analyzes the nature of the residual errors but assumes their random nature and obedience to the classical normal distribution. One of the methods for analyzing the time series of coordinates with residual, unaccounted-for systematic errors is the non-classical error theory of measurements. The result of this work is a developed software solution for analyzing the time series of GNSS coordinates to test their normality, or in other words, to test whether a particular GNSS station is subject to the influence of small, unaccounted-for errors. Conclusions: After testing our software on four reference stations in Europe, we concluded that none of the chosen stations followed the normal law of distribution; thus, it is vital to perform such tests before conducting any experiments on the time series from reference stations. [ABSTRACT FROM AUTHOR]

The signal-in-space range error (SISRE) has a direct impact on the performance of global navigation satellite systems (GNSSs). It is an important indicator of navigation satellite space server performance. The new B-CNAV navigation messages (B-CNAV1 and B-CNAV2) are broadcast on the satellites of the Beidou Global Navigation Satellite System (BDS-3), and they are different from D1 navigation messages in satellite orbit parameters. The orbit accuracy of B-CNAV navigation messages lacks analyses and comparisons with D1. The accuracy and stability of the new hydrogen and rubidium clocks on BDS-3 satellites need annual analyses of long time series, which will affect the service quality of this system. Based on precise ephemeris products from the Center for Orbit Determination in Europe (COD), the orbit error, clock error, and SISRE of 24 medium Earth orbit (MEO) satellite D1 and B-CNAV navigation messages of BDS-3 were computed, analyzed, and compared. Their annual evolution processes for the entire year of 2022 were studied. Thanks to the use of inter-satellite links (ISLs) adopted by BDS-3 MEO satellites, the ages of the ephemeris are accurate and the percent of ages of data, ephemerides (AODEs), and ages of data and clocks (AODCs) shorter than 12 h were 99.95% and 99.96%, respectively. In addition, the broadcast orbit performance was also improved by ISLs. The root mean square (RMS) values of the BDS-3 MEO broadcast ephemeris orbit error were 0.067 m, 0.273 m, and 0.297 m in the radial, cross, and along directions, respectively. Moreover, the 3D RMS value was 0.450 m. Thanks to the use of new orbit parameters in the B-CNAV navigation messages of BDS-3 MEO, its satellite orbit accuracy was obviously better than that of D1 in the radial direction. Its improved accuracy can reach up to about 1.2 cm, and the percentage of its accuracy improvement was about 19.06%. With respect to clock errors, the timescale differences between the two clock products were eliminated to assess the accuracy of broadcasting ephemeris clock errors. A standard deviation value of 0.256 m shows good performances as a result of the use of the two new types of atomic clocks, although the RMS value was 0.541 m due to a nonzero mean bias. Overall, the accuracy of atomic clocks was good. For the new hydrogen and rubidium atomic clocks, their RMS and standard deviation were 0.563 m and 0.231 m and 0.519 m and 0.281 m, respectively. The stability of the former was better than that of the latter. However, due to the nonzero mean bias the latter was better than the former in accuracy. The RMS value of the SISRE of BDS-3 MEO's broadcast ephemeris was 0.556 m, and the value was 0.920 m when it had a 95% confidence level. In contrast, after deducting the influence of the clock error, the value of SISRE_ORB was 0.092 m. Since the satellite clock error was substantially larger than the orbit radial error, the SISRE was mainly affected by the clock error, and their annual evolutions were consistent. Because of the improvement to the B-CNAV's navigation message with respect to orbit radial accuracy, SISRE_ORB has improved in accuracy. Compared to D1, it had a significant effect on improving the accuracy of SISRE_ORB, and the percentage of the accuracy improvement was 8.40%. [ABSTRACT FROM AUTHOR]